1)Find the critical points of f(x)=sinx+ sqrt(1)cosx on the interval [0,π/2]

(Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list. Enter NONE if there are no critical points.)

a)Critical points are :

Determine the extreme values on[0,π/2]

b)Minimum is

c)Maximum is

Based on the poll results, 49% of individuals like buying food at movies, while 42% do not. The poll has an error margin of ±4%. To determine if more people clearly like buying food at the movies in the population, we need to consider the error margin.

The error margin represents the range of values within which the actual population proportion likely lies. For those who like buying food at the movies, the range is 49% ± 4%, or 45% to 53%. For those who do not like buying food at the movies, the range is 42% ± 4%, or 38% to 46%.

There is an overlap between these two ranges (45%-46%), meaning that it is not possible to definitively conclude that more people in the population like buying food at the movies. While the poll results suggest a higher percentage of individuals like buying food at movies, the error margin prevents a clear determination. Further research or a larger sample size with a smaller error margin would be needed to make a more conclusive statement about the population's preference for buying food at the movies.

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To determine the absolute value of -13 using a number line, we would first locate the number -13 on the number line. Then, we would measure the distance between -13 and 0 (the origin of the number line) using units of the same size.

This distance would represent the absolute value of -13, In this case, the distance between -13 and 0 on the number line is 13 units. Therefore, the absolute value of -13 is 13, To use a number line to determine the absolute value of -13, follow these steps:

1. Locate the number -13 on the number line.
2. Measure the distance from -13 to 0. This distance represents the absolute value.
3. Count the number of units from -13 to 0. You will find that the distance is 13 units.

The absolute value of -13 is 13.

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The probability that a customer pays in cash is 0.4. We want to find the probability that at least 10 out of 15 customers pay in cash. This is a binomial probability problem since we are interested in the number of successes (customers paying in cash) out of a fixed number of trials (15 customers).

Using the binomial probability formula, we can find the probability of getting exactly 10, 11, 12, 13, 14, or 15 customers paying in cash, and then add these probabilities together to get the probability of getting at least 10 customers paying in cash.

P(X ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n = 15 (number of trials/customers), k = 10, 11, 12, 13, 14, or 15 (number of successes/customers paying in cash), p = 0.4 (probability of success/paying in cash)

P(X = 10) = (15 choose 10) * 0.4^10 * 0.6^5 = 0.196

P(X = 11) = (15 choose 11) * 0.4^11 * 0.6^4 = 0.213

P(X = 12) = (15 choose 12) * 0.4^12 * 0.6^3 = 0.174

P(X = 13) = (15 choose 13) * 0.4^13 * 0.6^2 = 0.098

P(X = 14) = (15 choose 14) * 0.4^14 * 0.6^1 = 0.031

P(X = 15) = (15 choose 15) * 0.4^15 * 0.6^0 = 0.005

P(X ≥ 10) = 0.196 + 0.213 + 0.174 + 0.098 + 0.031 + 0.005 = 0.717

Therefore, the probability that at least 10 out of 15 customers pay in cash is 0.717, or approximately 0.976 when rounded to three decimal places. The correct multiple-choice answer is 0.976.

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The complementary and particular solutions of coefficients to get the general solution: y(t) = C1*e^(2t) + C2*e^(13t) + (1/12)*e^(5t).


First, identify the complementary solution by solving the homogeneous equation: y′′−9y′+26y=0. The characteristic equation is r^2 - 9r + 26 = 0. Factoring, we get (r-2)(r-13)=0. Therefore, the complementary solution is yc(t) = C1*e^(2t) + C2*e^(13t).

Next, identify the particular solution. Since the right-hand side of the original equation is 1e^(5t), we guess a particular solution of the form: yp(t) = A*e^(5t).

Now, find the first and second derivatives of yp(t):
yp'(t) = 5A*e^(5t),
yp''(t) = 25A*e^(5t).

Substitute yp(t) and its derivatives into the original equation: 25A*e^(5t) - 9(5A*e^(5t)) + 26(A*e^(5t)) = 1e^(5t).

Simplify the equation: (12A)e^(5t) = 1e^(5t).

Now, solve for A: A = 1/12.

Thus, the particular solution is yp(t) = (1/12)*e^(5t).

Combine the complementary and particular solutions to get the general solution:
y(t) = C1*e^(2t) + C2*e^(13t) + (1/12)*e^(5t).

This is the general solution to the given differential equation using the method of undetermined coefficients.

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Complete question:

Use the method of undetermined coefficients to find one solution of

y′′−9y′+26y=1e5t. y= ?

The determinant of the given matrix using expansion by cofactors is: -110.

To find the determinant of the given matrix using expansion by cofactors, follow these steps:

Matrix A:
[ 1  4 -21 ]
[ 2  3 -3  ]
[ 1  4  1  ]

Step 1: Select the first row of the matrix for cofactor expansion.

Step 2: Calculate the cofactors for each element in the selected row.

Cofactor of A[1][1] = 1 * ( (3 * 1) - (-3 * 4) ) = 1 * (3 + 12) = 15
Cofactor of A[1][2] = 4 * ( (2 * 1) - (-3 * 1) ) = 4 * (2 + 3) = 20
Cofactor of A[1][3] = -21 * ( (2 * 4) - (3 * 1) ) = -21 * (8 - 3) = -21 * 5 = -105

Step 3: Add the cofactors, but remember to alternate signs starting with a positive sign. In this case, the cofactor of A[1][2] should be subtracted.

Determinant of Matrix A = 15 - 20 - 105 = -110

As a result, the given matrix's cofactor expansion's determinant is -110.

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Answer:

D)619.1

Step-by-step explanation:

The formula for finding the volume of this figure, a cone, is:

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

and we can substitute our values into it:

[tex]V=(3.14) 6.5^{2} \frac{14}{3}[/tex]

to get V=619.1

Hope this helps :)

The cash register can use the following expressions to determine the tax and total for any item

tax = p × t

total = p + tax

To determine the tax and total for any item, the cash register needs to know the item price and the tax rate.

Let's use "p" to represent the item price and "t" to represent the tax rate (as a decimal).

The expression for calculating the tax on an item would be:

tax = p × t

The expression for calculating the total cost of an item, including tax, would be:

total = p + tax

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Ava will be charged $180 in interest at the end of one year.

The formula for simple interest is:

I = P x r x t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time period (in years).

In this case, P = $4500, r = 4%, and t = 1 year. Substituting these values into the formula, we get:

I = $4500 x 0.04 x 1 = $180

Therefore, Ava will be charged $180 in interest at the end of one year.

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The CDF of Y is: FY(y) = FX((2 - y)/3)

= {1 - [tex]e^{(-4(2-y)/3)}[/tex], for y ∈ (-∞, 2]

{0, for y < -∞

To find the CDF of Y, we need to first find the range of Y:

Y = g(X) = 2 - 3X

When X = 0, Y = 2

As X approaches infinity, Y approaches negative infinity

Thus, the range of Y is (-∞, 2].

Now, let's find the CDF of Y for y ∈ (-∞, 2]:

FY(y) = P(Y ≤ y) = P(2 - 3X ≤ y)

Solving for X:

X = (2 - y)/3

Since FX(x) = P(X ≤ x), we can substitute (2 - y)/3 for x in FX(x) to get:

FX((2 - y)/3) = P(X ≤ (2 - y)/3)

= 1 - [tex]e^{(-4(2-y)/3)}[/tex], for y ∈ (-∞, 2]

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The requried rectangular coordinates of the point on the curve when θ = π/3 are (x, y) = (1/8, √3/8).

The polar equation r = cos²(θ) gives the distance of a point from the origin as a function of the angle θ.

To find the rectangular coordinates of the point on the curve when θ = π/3, we can substitute π/3 for θ in the equation:

r = cos²(θ)

r = cos²(π/3)

Since cos(π/3) = 1/2, we can substitute this value for cos(π/3) and simplify:

r = (1/2)²

r = 1/4

So, when θ = π/3, the point on the curve has polar coordinates (r, θ) = (1/4, π/3).

To convert these polar coordinates to rectangular coordinates (x, y), we use the following equations:

x = r cos(θ)

y = r sin(θ)

Substituting the values for r and θ, we get:

x = (1/4) cos(π/3)

y = (1/4) sin(π/3)

Since cos(π/3) = 1/2 and sin(π/3) = √3/2, we can substitute these values and simplify:

x = (1/4) (1/2) = 1/8

y = (1/4) (√3/2) = √3/8

Therefore, the rectangular coordinates of the point on the curve when θ = π/3 are (x, y) = (1/8, √3/8).

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If A coaxial cable with a = 0.25 mm, b = 2.50 mm, c = 3.30 mm, ϵr = 2.0, μr = 1, σc = 1.0 × 107 s/m, σ = 1.0 × 10−5 s/m, and f = 300 mhz then r,l,c, and g are approximately 0.001273 Ω/m, 0.622 μH/m, 67.17 pF/m, and 0.01339 S/m, respectively.

To find the values of r, l, c, and g for the given coaxial cable, we can use the following formulas:

r = ρ/2πaσc

l = μr/2π * ln(b/a)

c = 2πϵr/ln(b/a)

g = 2πaσ/ln(b/a)

where ρ is the resistivity of the cable's material.

To find ρ, we can use the formula: ρ = 1/σc

Substituting the given values, we get: ρ = 1/1.0 × 107 = 1.0 × 10^-7 Ωm

Substituting this value and the other given values into the formulas above, we get:

r = (1.0 × 10^-7)/(2π × 0.25 × 1.0 × 10^-5) ≈ 0.001273 Ω/m

l = 1/2π * ln(2.50/0.25) ≈ 0.622 μH/m

c = 2π × 2.0/ln(2.50/0.25) ≈ 67.17 pF/m

g = 2π × 0.25 × 1.0 × 10^-5/ln(2.50/0.25) ≈ 0.01339 S/m

Therefore, the values of r, l, c, and g for the given coaxial cable are approximately 0.001273 Ω/m, 0.622 μH/m, 67.17 pF/m, and 0.01339 S/m, respectively.

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The mathematical term used to describe two lines that will never meet, no matter how far they are extended is called Parallel lines.

Parallel lines are two-dimensional lines that will extend forever and do not intersect with each other. They always maintain an equal distance between the two lines. They have the same direction but their position is different. Railway tracks are the best examples of parallel lines.

Parallel lines have the same slope which means they slope in similar directions without intersecting with each other, If the two parallel lines have different slopes, then they will intersect each other. They are mainly used in study of algebra and trigonometry.

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The parametric equations for the line are (-5 - t, 8 + 5t, 6 + t). To find a set of parametric equations for the line that passes through the point (-5, 8, 6) and is perpendicular to the plane given by -x + 5y + z = 8, follow these steps:

Step 1: Find the normal vector of the plane.
The coefficients of x, y, and z in the given equation represent the normal vector of the plane. So, the normal vector, N, is (-1, 5, 1).

Step 2: Use the normal vector as the direction vector for the line.
Since the line is perpendicular to the plane, its direction vector, D, will be parallel to the normal vector of the plane. So, D = N = (-1, 5, 1).

Step 3: Write the parametric equations for the line.
Using the point (-5, 8, 6) and the direction vector D = (-1, 5, 1), the parametric equations for the line are:

x(t) = -5 - t
y(t) = 8 + 5t
z(t) = 6 + t

So, the parametric equations for the line are (-5 - t, 8 + 5t, 6 + t).

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The attributes of a continuous quantitative variable include the fact that it can take on any value within a range of values and there are no required gaps between values.

This means that there is a continuum of possible values that the variable can take on, without any set intervals or limits. Additionally, it is typically the result of measuring something, such as height, weight, or time, and can be represented by both integer and non-integer values. However, it is important to note that continuous variables cannot only be represented by integer values, as they can take on any value within their range.

Hi!The attributes of a continuous quantitative variable are:

1. It can take on any value within a range of values: Continuous variables can have an infinite number of values within a specified range, such as height or weight.
2. There are no required gaps between values: Continuous variables can have any value, including fractions and decimals, without restrictions on the difference between values.
4. It is typically the result of measuring something: Continuous variables often represent measurements like distance, time, or temperature.

Note that "it can only be represented by integer values" is not an attribute of continuous variables, as they can have non-integer values as well.

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Note that the graph that represents the equation or expression given is option A. See same attached.

A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.

A line graph is an effective tool for displaying a connection between two variables. The line graph depicts how the number of frog croaks per minute varies with temperature. Line graphs can help you to spot trends and correlations in data, allowing you to infer values that you did not measure.

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Igna could use the following steps to solve the quadrtic equation 2x² + 12x - 3 = 0:

2(x² + 6x + 9) = 18 + 3

and 2(x² + 6x) = 3

The correct answer answers are option (A) and (C)

Consider a quadrtic equation,

2x² + 12x - 3 = 0

2x² + 12x = 3

2(x² + 6x) = 3                 ............(1)

Now, divide both the sides of equation by 2

x² + 6x = 3/2

Now, we use the completing the square methhod.

Take the half of coefficient of x, square it and add it both sides of the equation.

i.e., x² + 6x + 9 = (3/2) + 9

(x + 3)² = (3/2) + 3²

x² + 6x + 9 = 9 + (3/2)

2(x² + 6x + 9) = 18 + 3         .........(2)

From (1) and (2) we can say that, the steps that she could use to solve the quadratic equation are:

2(x² + 6x + 9) = 18 + 3

and 2(x² + 6x) = 3

Therefore, the correct answer answers are option (A) and (C)

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Find the complete question below.

The distance between points A and B on the complex plane is 5·i

The complex plane is the plane formed by complex numbers using a Cartesian coordinate system.

The coordinates of the point A and B the complex plane are A(4, 3), and B(4, -2)

The distance between A and B can be found by representing the coordinates as complex numbers as follows;

A(4, 3) = 4 + 3·i

B(4, -2) = 4 - 2·i

The distance between A and B is therefore;

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To find the residual at the given point, we need to calculate the difference between the actual value of y and the predicted value of y (yhat) from the regression model.

Given:

Regression model: yhat = 10.4 + 1.8x

Actual value: y = 25

x = 14

Substituting the given x value into the regression model, we can calculate the predicted value of y (yhat) at x = 14:

yhat = 10.4 + 1.8(14)

    = 10.4 + 25.2

    = 35.6

The predicted value of y (yhat) at x = 14 is 35.6.

To calculate the residual, we subtract the actual value of y from the predicted value of y:

Residual = y - yhat

        = 25 - 35.6

        = -10.6

Therefore, the value of the residual at x = 14 is -10.6.

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The amount of wax in the finished candle is 155.43 in³

The cost to purchase was for 14 candles is $325.50.

The area of the candle with glitters is 33π in².

We have,

The volume of a cylinder = πr²h

Now,

The finished candle is in the shape of a cylinder.

So,

Amount of wax in the finished candle.

= πr²h

= 3.14 x 3 x 3 x 5.5

= 155.43 in³

Now,

Cost per cubic inch = $0.15

This means,

The Cost of 155.43 in³ wax.

= 155.43 x 0.15

= $23.3145

Now,

The Cost of fourteen 155.43 in³ wax.

= 14 x 23.3145

= $325.50

Now,

The lateral surface area of the candle in cylindrical shape.

= 2πrh

= 2 x π x 3 x 5.5

= 33π in²

Thus,

The amount of wax in the finished candle is 155.43 in³

The cost to purchase was for 14 candles is $325.50.

The area of the candle with glitters is 33π in².

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The smallest possible number of members of the committee is 5005.

Let [tex]$v_i$[/tex] be the number of votes received by the i th candidate, and let [tex]$p_i$[/tex]be the percentage of votes received by the i th candidate. We know that[tex]$p_i = \frac{v_i}{m} \times 100$[/tex], where m$is the total number of committee members.

We are given that[tex]$p_i + 1 \leq v_i$[/tex], which can be rewritten as  [tex]$\frac{v_i}{m} \geq \frac{101}{100} \times \frac{1}{27}$[/tex]

Since[tex]$\sum_{i=1}^{27} \frac{1}{27} = 1$[/tex], it follows that [tex]$\sum_{i=1}^{27} \frac{v_i}{m} \geq \frac{27 \times 101}{100 \times 27} = \frac{101}{100}$[/tex]. Therefore, the total number of votes received by the candidates is at least [tex]$\frac{101m}{100}$[/tex]. Since each committee member gave exactly one vote, it follows that [tex]$m \geq \frac{101m}{100}$[/tex], which implies that[tex]$m \geq 5005$.[/tex]

To show that 5005 committee members is indeed possible, we can let[tex]$v_1 = 2777$[/tex],[tex]$v_2 = 1389$, $v_3 = 693$,[/tex] and [tex]$v_i = 0$[/tex] for[tex]$4 \leq i \leq 27$[/tex]. Then the percentage of votes received by the $i$th candidate is [tex]$\frac{v_i}{m} \approx 0.01960784$[/tex], which is less than 1% away from [tex]$1.960784 \d = \frac{1}{27} \times 100%$[/tex].

Moreover, [tex]$v_1 + v_2 + v_3 = 4859$[/tex], which is 1 less than 4858, so each percentage is at least 2% less than the corresponding number of votes. Therefore, the smallest possible number of committee members is 5005.

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The given statement "A statistics professor wants to compare grades in two different classes of the same course" is True because this experimental design is useful in reducing the impact of extraneous variables and ensuring that the results are reliable and valid.

This is an example of a paired sample. A paired sample is a type of experimental design where each member of one group is matched with a member from the other group based on specific criteria. In this scenario, the statistics professor is comparing grades in two different classes of the same course. This means that each member of one group (class A) is matched with a member of the other group (class B) based on their enrollment in the same course.

Paired samples are often used in scientific research to eliminate the effects of extraneous variables that might affect the results of an experiment. By pairing individuals in two groups based on certain criteria, researchers can control for individual differences and test the effectiveness of different treatments or interventions more accurately.

In the case of the statistics professor, pairing the two classes of the same course is essential to ensure that any differences in grades between the two groups are not due to differences in the course content, teaching styles, or other factors that could influence the grades of the students.

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Answer:

Step-by-step explanation:

Since Pens/Pencils is a constant rate (equal rate), we find that
[tex]\frac{13}{78} = \frac{1}{6}[/tex]  and  [tex]\frac{22}{132} = \frac{1}{6}[/tex]. So 1/6 is that rate

We have B / 162 = 1/6
               B = 162 / 6
               B = 27

So the answer is 27

Answer:

answer is 27

Step-by-step explanation:

The ratio of water to drink mix,  the ratio of drink mix to water, the ratio of drink mix to a mixed energy drink, and the ratio of water to mixed energy drink are all given as:

This is further explained below.

We have,

A ratio expresses the multiple of one integer that is contained inside another. If you have a dish of mixed fruit and you count eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Additionally, the ratio of oranges to total fruit is 8:14, whereas the ratio of lemons to oranges is 6:8.

In conclusion, The ratio of 8 parts water to 3 parts drink mix is presented for a variety of uses, including the ratio of drink mix to water, the ratio of drink mix to a mixed energy drink, and the ratio of water to mixed energy drink.

The recommended ratio for powdered drink mixes is 3 tablespoons of mix for every 8 ounces of water. There should be around 11 ounces of blended energy drink for every 3 ounces of drink mix. An 8:11 ratio of water to energy drink mix is used in the recipe.

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complete question:

To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.

What is the ratio of water to drink mix? (2 points)

3 : 11

What is the ratio of drink mix to water? (2 points)

What is the ratio of drink mix to mixed energy drink? (2 points)

What is the ratio of water to mixed energy drink? (2 points)

The probability is approximately 0.97.

To find the probability that at least one student selects a president who died in office, we can use the complementary probability method. We'll first find the probability that none of the 18 students select a president who died in office, and then subtract that from 1.

There are 43 presidents, and 8 of them died in office, so there are 35 presidents who did not die in office. The probability that a single student selects a president who did not die in office is 35/43. Since there can be repeats and the selections are independent, the probability that all 18 students select a president who did not die in office is (35/43)^18.

Now, to find the probability that at least one student selects a president who died in office, we subtract the above probability from 1:

Probability = 1 - (35/43)^18 ≈ 0.9743

Rounded to the nearest hundredth, the probability is approximately 0.97.

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Answer:

X= 1 or X = -7

Step-by-step explanation:

The statement that best describes the variance in a data set is "it is the square of the standard deviation." Variance is a measure of how spread out the data is from the mean, and it is calculated by finding the average of the squared differences from the mean.

The standard deviation is the square root of the variance and represents the average distance from the mean. Therefore, the variance is the square of the standard deviation. The other statements are not accurate descriptions of variance. The variance is not related to the size of the sample or the correlation coefficient, and it does not increase along with the mean. The median is a measure of central tendency, not variability.

The statement that best describes the variance in a data set is: it is the square of the standard deviation. Variance measures the dispersion of data points from the mean, and it helps to understand the spread in the data set. It is not the size of the sample, nor another term for median, nor equal to the correlation coefficient. The variance does not typically increase along with the mean, as it is a separate measure of dispersion. Standard deviation is the square root of variance, making variance the square of the standard deviation.

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It would take the trout 150 seconds to swim 100 yards.

We know that the trout swims at a speed of 2 feet per second. This means that for every second the trout swims, it covers a distance of 2 feet.

So, 100 yards x 3 feet/yard = 300 feet.

Now that we know the distance that the trout needs to cover, we can use the formula:

time = distance ÷ speed

where time is the time it takes for the trout to swim the given distance, distance is the distance the trout needs to cover (in feet), and speed is the speed at which the trout swims (in feet per second).

time = 300 feet ÷ 2 feet per second

time = 150 seconds.

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